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Chapter 6: Q. 6.14 (page 570)

Factor by grouping:ab+7b+8a+56

Short Answer

Expert verified

The factored form is(a+7)(b+8).

Step by step solution

01

Step 1. Given Information

The given expression isab+7b+8a+56

02

Step 2. Rewrite the given expression 

  • All four terms do not have the greatest common factor.
  • Factor the GCF, bfrom the first 2 terms of the given expression.

b(a+7)+8a+56

  • Factor the GCF, 8 from the last two terms of the obtained expression.

b(a+7)+8(a+7)

  • Factor out the common factor a+7in the obtained expression.

role="math" localid="1644906320140" b(a+7)+8(a+7)=(a+7)(b+8)

03

Step 3. Check

  • Multiply the obtained factors.

(a+7)(b+8)=ab+8a+7b+56=ab+7b+8a+56

  • Since the obtained expression is the same as the given expression, the obtained factors are verified.

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